A motorboat whose speed is $18$ km/h in still water takes $1$ hour more to go $24$ km upstream than to return downstream to the same spot. Find the speed of the stream.

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Step 1: Let speed of the stream be $x$ km/h. Upstream speed $= (18 - x)$, downstream speed $= (18 + x)$.
Step 2: $\frac{24}{18 - x} - \frac{24}{18 + x} = 1$
Step 3: $\Rightarrow 24(18 + x) - 24(18 - x) = (18 - x)(18 + x) \Rightarrow 48x = 324 - x^2$
Step 4: $\Rightarrow x^2 + 48x - 324 = 0 \Rightarrow (x + 54)(x - 6) = 0$
Step 5: $x = 6$ (rejecting $x = -54$). Speed of stream $= 6$ km/h.

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